High frequency ventilation (HFV), which utilizes small tidal volumes at rapid rates, is an innovative method of ventilation that possesses certain advantages desired by anesthesiologists and intensivists. The fluid dynamic mechanisms responsible for gas exchange in HFV are not well understood, but one observation is that airway geometry near a bifucation induces a steady net fluid drift from pure oscillatory cycling. This steady drift is bi-directional, potentially providing a means for bulk, convective transport of both oxygen and carbon dioxide. The research proposed here examines the fluid mechanics and mass transfer of oscillatory flow in a divergent channel or tube. The divergence slope Epsilon is small (Epsilon is dominated by 1) and represents the slightly tapered, distal end of an airway just prior to a bifurcation. A theoretical analysis employs regular and singular perturbation methods, standard techniques of applied mathematics, to solve the governing, non-linear equations of motion for Beta2 is dominated by 1 and Beta2 is dominated by 1 where Beta is the Womersley number. Preliminary theoretical results predict bi-directional, steady fluid motion which is consistent with observations. A sequence of progressively more complicated analyses is posed to illuminate the mechanisms responsible for this non-linear, convective transport phenomenon. Experiments of oscillating flow in a divergent channel or tube are outlined to test the theory by measuring the steady drift velocities for representative value of Epsilon and Beta2.